Concurrent topology optimization of composite macrostructure and microstructure under uncertain dynamic loads

Multiscale structure has attracted significant interest due to its high stiffness/strength to weight ratios and multifunctional performance. However, most of the existing concurrent topology optimization works are carried out under deterministic load conditions. Hence, this paper proposes a robust concurrent topology optimization method based on the bi-directional evolutionary structural optimization (BESO) method for the design of structures composed of periodic microstructures subjected to uncertain dynamic loads. The robust objective function is defined as the weighted sum of the mean and standard deviation of the module of dynamic structural compliance with constraints are imposed to both macro-and micro-scale structure volume fractions. The polynomial chaos expansion (PCE) method is used to quantify and propagate load uncertainty to evaluate the objective function. The effective properties of microstructure is evaluated by the numerical homogenization method. To release the computation burden, the decoupled sensitivity analysis method is proposed for microscale design variables. The proposed method is a non-intrusive method, and it can be conveniently extended to many topology optimization problems with other distributions. Several numerical examples are used to validate the effectiveness of the proposed robust concurrent topology optimization method.